Unbalance & neutral current
The key idea
On a four-wire wye system the neutral carries the vector sum of the three phase currents. Load the phases equally and that sum is zero: the neutral sits empty. Load them unequally, and the difference flows in the neutral.
The idea
A balanced three-phase load needs no return conductor at all. Three equal currents, 120° apart, add to exactly zero at every instant. That cancellation is the whole advantage of three-phase: three times the power of a single-phase system on wires of the same size.
Real low-voltage feeders are not balanced. Most of their load is single-phase: socket circuits, lighting, a water heater, an EV charger, each connected between one phase and the neutral, and none of it switching on in tidy groups of three. So a four-wire wye system keeps a neutral conductor, and whatever the three phases fail to cancel flows in it.
Neutral current is the vector sum of the three phase currents: Kirchhoff's current law at the star point. The word vector matters. The three currents point 120° apart, so they do not subtract like ordinary numbers: put 40, 60 and 80 A on the phases and the neutral carries not 80 − 40 = 40 A but 34.6 A, at an angle that matches no phase.
Symmetrical components describe the same fact another way. The zero-sequence current is exactly one third of the neutral current: zero sequence is three currents in step, a pattern that cannot cancel and must return through a conductor. Unequal load also produces negative-sequence current, a balanced set rotating the wrong way. Equipment responds to both: negative sequence heats rotating machines, and earth-fault relays measure zero sequence.
The remedy is rarely electrical. Redistribute the single-phase loads across the phases until the three are close to equal. The total demand does not change and no new equipment is needed — but the neutral current falls, the negative sequence disappears, and the losses in the neutral conductor go with them.
Try it
Pull the three loads apart and watch the dashed neutral arrow appear. Then press Balance the load — same total demand, equal phases, empty neutral.
neutral current |IN|
34.6 A
unbalance factor
19.2 %
status
unbalanced
The neutral carries the vector sum of the three phase currents and nothing else. Equal loads cancel, and the neutral is empty. Move load onto one phase, and the difference appears in the neutral and in the negative and zero sequence. The neutral current can reach the full current of one phase. Every phase here is at unity power factor, so the arrows stay at 0°, −120° and +120° and only their lengths change. Real unbalance changes the angles as well.
Why it matters
- The neutral is not a spare wire. A badly distributed single-phase load can put as much current in the neutral as in a phase, which is why engineers size the neutral as a full phase conductor, with triplen harmonics adding their own contribution on top. A switch or fuse in the neutral alone is worse still: if the neutral opens under unbalance, the phase voltages redistribute across the loads, and the lightly loaded phase rises toward line voltage.
- Negative sequence overheats motors. An induction motor offers very little impedance to a field turning the wrong way: that field sweeps past the rotor at nearly twice synchronous speed, so a few percent of negative sequence drives a large rotor current that makes heat and no useful torque. Motor protection relays measure negative sequence directly for exactly this reason.
- Zero sequence looks like an earth fault. Residual earth-fault protection adds the three phase currents — the identical sum. A permanent unbalance therefore sits inside the measurement, eating the margin between normal operation and the relay setting.
- Unbalance spreads to other customers. An unbalanced current through the source impedance makes an unbalanced voltage drop, so the phase voltages at the busbar are no longer equal, and every other customer on the feeder receives the unbalance as a supply problem.
The math, if you want itOptional — the page reads completely without it
Kirchhoff's current law at the star point of a four-wire wye:
neutral current
IN = IA + IB + IC
— a sum of phasors, not of magnitudes. The widget puts every phase at unity power factor, so the currents keep their nominal angles and only the magnitudes change:
the model on this page
IN = IA∠0° + IB∠−120° + IC∠+120°
The same three currents, written in symmetrical components with the rotation operator a = 1∠120°:
positive sequence
I₁ = ⅓ ( IA + a·IB + a²·IC )
negative sequence
I₂ = ⅓ ( IA + a²·IB + a·IC )
zero sequence
I₀ = ⅓ ( IA + IB + IC )
The last equation is the neutral current divided by three; the two quantities are the same thing:
neutral and zero sequence
IN = 3 · I₀
The standard measure of how much unbalance there is:
current unbalance factor
100 · |I₂||I₁| %
The unity-power-factor simplification has two visible consequences in the widget: I₁ becomes the plain average of the three magnitudes, and |I₂| always equals |I₀|: the negative and zero bars keep the same length. Neither holds once the phases differ in power factor as well as magnitude, and a real feeder differs in both. The shape of the result survives; the exact numbers do not.
See it in Phasor
A power flow is a balanced, positive-sequence study: it assumes the cancellation this page describes, which is exactly what lets one line on the single-line diagram stand for three conductors and a neutral. Check that assumption against the feeder you model: if the real load is a long row of single-phase connections, the phase current Phasor reports is an average of three unequal currents, and the neutral current it never draws can still be tens of amps.